Correcting Aliasing of Pulsed Wave Doppler of Diagnostic Ultrasound

ABSTRACT

Pulsed wave (PW) Doppler has the same emitted and reflected pulse frequency because it emits the next ultrasound pulse after receiving the previously reflected one. But, the forward blood flow will interact with the emitted ultrasound pulse and shorten its time of flight (TOF), which creates a positive TOF shift between the calculated TOF and detected TOF. If the velocity of forward flow is too fast and causes the TOF shift more than half of the calculated TOF, the reflected ultrasound pulses are considered as from the previously emitted pulses with longer TOF, which will show negative TOF shift and be misinterpreted as aliasing. This aliasing TOF shift can be completely rectified to its correct registration no matter how fast the forward flow velocity will be. So, the advantages of TOF shift theory can better quantitatively explain the spectral characteristics of PW Doppler, and more accurately calculate the flow velocity.

CROSS-REFERENCE TO RELATED APPLICATIONS

Mechanism in Corecting Aliasing of Pulsed Wave Doppler of Diagnostic Ultrasound. Provisional patent, Application No.: U.S. 61/508,333; Filing Date: Jul. 15, 2011

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

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REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISC APPENDIX

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BACKGROUND OF THE INVENTION

Continuous wave (CW) Doppler and pulsed wave (PW) Doppler work with different ultrasound mechanisms. By sending continuous waves, CW Doppler system detects reflected frequency in the area under the transducer. Doppler shift is calculated by extracting the transmitted frequency from reflected frequency. If the flow is toward the transducer, the reflected waves will be compressed, which generates higher reflected frequency and positive Doppler shift. Because of the separation of emitting and receiving components, continuously receiving reflected ultrasound pulses avoids it generating aliasing.

However, the pulsed wave (PW) Doppler has different mechanism. PW Doppler uses only one PZT crystal in sending and receiving ultrasound pulses. Then it calculates the TOF of the ultrasound pulses corresponding to the depth of the gate. This brings its advantage of range specificity as well as its disadvantage of aliasing. Aliasing of PW Doppler can be explained with the insufficient Doppler sampling rate of the frequency domain analysis or misinterpreted TOF shift of the time domain analysis. But, the theory of frequency domain can not completely solve the aliasing. For time domain analysis, the PW Doppler works more like playing table tennis, because its transducer will emit the next ultrasound pulse after receiving the previously reflected one. If an ultrasound pulse hits on an object at a designated distance, the ultrasound system can calculate its TOF based on the ultrasound speed and the distance. If the ultrasound pulse hits a forward object, the object will interact with the pulse and shorten its traveling distance and TOF. So, there is a TOF shift between the detected TOF and calculated TOF. Faster the forward object is, the more TOF shift will be. Therefore, I use TOF shift to explain and rectify the aliasing of PW Doppler system.

BRIEF SUMMARY OF THE INVENTION

The object of the present invention is explaining the aliasing of PW Doppler with TOF shift of time domain analysis. Based on TOF shift theory, the aliasing can be completely corrected.

In order to attain the above object, according to a first aspect of the present invention, the PW Doppler system calculates TOF according to the detecting depth and propagation speed. The forward flow will interact with ultrasound pulses and shorten their traveling distance and detected TOF. So, the Doppler shift is caused by TOF shift between calculated TOF and detected TOF, which is produced by forward flow.

According to a second aspect of the present invention, if the forward flow is too fast, it increases the detected TOF shift more than half of the value of calculated TOF. The Doppler system will misinterpret the reflected ultrasound pulses from the previously emitted pulses. The misinterpreted pulses have longer detected TOF, which generates negative TOF shift. So, the Doppler system account that the pulses are reflected from a reverse flow, which causes aliasing.

According to a third aspect of the present invention, the TOF shift is proportional to its spectrum, and aliasing TOF shift can be rectified to its correct registration. So, the aliasing can be completely corrected no matter how fast the flow velocity will be. At the same time, the method of TOF shift is more accurate in calculating flow velocity.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

Not Applicable

DETAILED DESCRIPTION OF THE INVENTION Doppler Shift of Pulsed Wave Doppler Is Based On TOF

The PW Doppler will locate the detecting depth and calculate TOF according to ultrasound speed and traveling distance. As playing table tennis, the forward flow will shorten the TOF of ultrasound pulses, and PW system will interpret the shortened TOF between calculated TOF and detected TOF as the TOF shift, which is directly correlated to the flow velocity. As range ambiguity artifacts in ultrasound imaging caused by speed error, the ultrasound system misinterprets the changed TOF as a changed detecting depth. In PW Doppler system, the changed TOF shift is connected with flow velocity, and the faster the forward flow velocity is, the greater TOF shift will be.

TOF shift=calculated TOF−detected TOF

In soft tissue:

Propagation  speed = 154, 000  cm/s P R F(Hz) = 77, 000  (cm/s)imaging  depth  (cm) $\begin{matrix} {{TOF} = {{Traveling}\mspace{14mu} {{distance}/{propagation}}\mspace{14mu} {speed}}} \\ {= {2 \times {imaging}\mspace{14mu} {{depth}/{propagation}}\mspace{14mu} {speed}}} \\ {= {{imaging}\mspace{14mu} {depth}\mspace{14mu} {({cm})/77},000\mspace{14mu} \left( {{cm}\text{/}s} \right)}} \\ {{TOP} = {{1/{PRF}} = {PRP}}} \end{matrix}$

The current PW Doppler system calculates its pulse repetition frequency (PRF) based on the pulse traveling speed and its detecting depth, which is inversely proportional to its TOF. Its emitted PRF is inversely proportional to its calculated TOF and its reflected PRF is inversely proportional to its detected TOF. So, decreased detected TOF due to increased forward flow velocity is interpreted as increased reflected PRF. But, the actual emitted and reflected pulse frequency doesn't change because the transducer emits the next pulse after receives the previous one.

Doppler  shift = reflected  P R F − emitted  P R F $\begin{matrix} {{{TOF}\mspace{14mu} {shift}} = {{{calculated}\mspace{14mu} {TOF}} - {{detected}\mspace{14mu} {TOF}}}} \\ {= {{{1/{emitted}}\mspace{14mu} P\; R\; F} - {{1/{reflected}}\mspace{14mu} P\; R\; F}}} \end{matrix}$

So, the Doppler shift is directly related to its TOF shift. But, the Doppler shift is not proportional to its TOF shift.

Aliasing Is Caused By Misinterpreting TOF Shift of Ultrasound Signals

Based on the current theory of aliasing, the aliasing is caused by too low Doppler sampling rate. If Doppler PRF is higher than its Nyquist limit (PRF/2), aliasing will occur. But, from my point of view, the aliasing is caused by too low detected TOF. For a forward flow, if the detected TOF is smaller than its detecting limits, the Doppler system will consider the reflected ultrasound pulse coming from previously emitted pulse with longer detected TOF. So, the TOF shift will be negative and the Doppler system misinterprets the pulses reflected from a reverse flow, which causes aliasing.

Aliasing  detected  TOF = actual  TOF + calculated  TOF $\begin{matrix} {{{Aliasing}\mspace{14mu} {TOF}\mspace{14mu} {shift}} = {{{calculated}\mspace{14mu} {TOF}} - {{aliasing}\mspace{14mu} {tested}\mspace{14mu} {TOF}}}} \\ {= {{{calculated}\mspace{14mu} {TOF}} - \left( {{{actual}\mspace{14mu} {TOF}} +} \right.}} \\ \left. {{calculated}\mspace{14mu} {TOF}} \right) \\ {= {{- {actual}}\mspace{14mu} {TOF}}} \end{matrix}$

So, for a forward flow, after exceeding the aliasing limit, its aliasing TOF shift is below the baseline and equals the value of actual TOF. The faster the flow is, the smaller the actual TOF will be. So, the value of aliasing Doppler shift will be smaller and is closer to the baseline. This tendency corresponds to the spectrum of aliasing, and also explains why the tip of aliasing spectrum is toward the baseline as increased flow velocity after passing its aliasing limit, which causes the inversely proportional relationship between the flow velocity and the value of aliasing TOF shift.

When  at  aliasing  limit, aliasing  TOF  shift = −calculated  TOF  shift      − actual  TOF = −(calculated  TOF − actual  TOF) $\mspace{79mu} {{{actual}\mspace{14mu} {TOF}} = {\frac{1}{2}\mspace{14mu} {calculated}\mspace{14mu} {TOF}}}$ $\begin{matrix} {\mspace{79mu} {{{TOF}\mspace{14mu} {shift}} = {{{calculated}\mspace{14mu} {TOF}} - {{actual}\mspace{14mu} {TOF}}}}} \\ {= {{{calculated}\mspace{14mu} {TOF}} - {{1/2}\mspace{14mu} {calculated}\mspace{14mu} {TOF}}}} \\ {= {\frac{1}{2}\mspace{20mu} {calculated}\mspace{14mu} {TOF}}} \end{matrix}$ $\begin{matrix} {\mspace{79mu} {{{Aliasing}\mspace{14mu} {TOF}\mspace{14mu} {shift}} = {{- {actual}}\mspace{14mu} {TOF}}}} \\ {= {{- \frac{1}{2}}\mspace{14mu} {calculated}\mspace{14mu} {TOF}}} \end{matrix}$

So, for a forward flow, if the detected TOF is smaller than half of its calculated TOF, the aliasing will appear. It is similar to Nyquist limit with emitted PRF reaching the half of reflected PRF. The aliasing TOF shift better explains why at the point of aliasing limit, the aliasing TOF shift has the similar value to TOF shift but at the opposite site of baseline. As increasing flow velocity after the aliasing limit, the actual TOF value will be smaller, which produces the specific aliasing spectrum with spectral tip toward baseline.

For a reverse flow, the detected TOF is greater than calculated TOF and TOF shift is negative. So, the Doppler system interprets it from a reversed flow. When the reverse flow is too fast, which makes the detected TOF excesses its aliasing limit, the Doppler system will misinterpret the reflected ultrasound pulse coming from the next emitted pulse.

Aliasing  detected  TOF = actual  TOF − calculated  TOF $\begin{matrix} {{{Aliasing}\mspace{14mu} {TOF}\mspace{14mu} {shift}} = {{{calculated}\mspace{14mu} {TOF}} - {{aliasing}\mspace{14mu} {detected}\mspace{14mu} {TOF}}}} \\ {= {{{calculated}\mspace{14mu} {TOF}} - \left( {{{actual}\mspace{14mu} {TOF}} -} \right.}} \\ \left. {{calculated}\mspace{14mu} {TOF}} \right) \\ {= {{2 \times {calculated}\mspace{14mu} {TOF}} - {{actual}\mspace{14mu} {TOF}}}} \end{matrix}$

So, aliasing TOF shift for a reverse flow will be positive, and its value will be reduced as increased flow velocity, which produces an aliasing spectrum above the baseline with its tip toward baseline.

At the point of aliasing limit:

      Aliasing  TOF  shift = −TOF  shift 2 × calculated  TOF − actual  TOF = −(calculated  TOF − actual  TOF) $\mspace{85mu} {{{actual}\mspace{14mu} {TOF}} = {1\frac{1}{2}\mspace{14mu} {calculated}\mspace{14mu} {TOF}}}$ $\begin{matrix} {\mspace{85mu} {{{TOF}\mspace{14mu} {shift}} = {{{calculated}\mspace{14mu} {TOF}} - {{actual}\mspace{14mu} {TOF}}}}} \\ {= {{{calculated}\mspace{14mu} {TOF}} - {1\frac{1}{2}\mspace{14mu} {calculated}\mspace{14mu} {TOF}}}} \\ {= {{- \frac{1}{2}}\mspace{14mu} {calculated}\mspace{14mu} {TOF}}} \end{matrix}$ $\begin{matrix} {\mspace{79mu} {{{Aliasing}\mspace{14mu} {TOF}\mspace{14mu} {shift}} = {{2\mspace{14mu} {calculated}\mspace{14mu} {TOF}} - {{actual}\mspace{14mu} {TOF}}}}} \\ {= {{2\mspace{14mu} {calculated}\mspace{14mu} {TOF}} - {1\frac{1}{2}\mspace{14mu} {calculated}\mspace{14mu} {TOF}}}} \\ {= {\frac{1}{2}\mspace{14mu} {calculated}\mspace{14mu} {TOF}}} \end{matrix}$

So, for a reverse flow, when its detected TOF is bigger than 1½ calculated TOF and its TOF shift approaches to ½ calculated TOF, it reaches to its aliasing limit and the reflected ultrasound pulses will be misinterpreted as from next emitted pulses, which causes aliasing.

So, the TOF shift for forward or reverse flow is limited within the value of one calculated TOF. If the TOF shift excesses the half of calculated TOF, the reflected ultrasound pulses are misinterpreted as aliasing.

Aliasing Can Be Completely Rectified By Correctly Registering Aliasing TOF

Nowadays, several ways, such as (1) adjust the scale to its maximum, (2) select a lower frequency transducer, or (3) select a new ultrasonic view with a shallower sample volume, are used to improve aliasing. These measures will reduce the calculated TOF, which can counteract some aliasing value at some degrees. But, if the velocity of the blood is very high, these methods can not completely correct aliasing, which is still beyond its aliasing limit. Based on our TOF shift theory, aliasing can be completely corrected by rectifying its registration accuracy.

For forward flow, after TOF shift excesses its aliasing limit:

Corrected TOF shift=calculated TOF−aliasing detected TOF

For reverse flow, after TOF shift excesses its aliasing limit:

Corrected TOF shift=aliasing detected TOF−calculated TOF

By modifying computer program of PW Doppler system to identify aliasing signals after exceeding the aliasing limit, their misinterpreted TOF can be rectified to their correct locations, which will completely correct aliasing no matter how fast the blood flow will be.

Comparing PRF shift, TOF shift better presents the spectrum of Doppler shift, and more accurately reflects its proportional relationship with the flow velocity. So, replacing Doppler shift with TOF shift in Doppler equation can more accurately calculate speed of blood.

The Doppler equation:

TOF shift=2×speed of blood×transducer frequency×cos Θ/propagation speed

TOF shift can completely correct aliasing and accurately calculate flow velocity. So, it can be applied in PW Doppler with higher frequencies. It not only avoids aliasing but also improves the quality of grayscale anatomic images in future PW Doppler system. 

1. Doppler shift of Pulsed wave Doppler is based on time of flight of ultrasound pulses
 2. Aliasing is caused by misinterpreting time of flight shift of ultrasound signals
 3. Aliasing can be completely rectified by correctly registering aliasing time of flight shift 